x^2-48x-578=0

Solution for x^2-48x-578=0 equation:

x^2-48x-578=0

a = 1; b = -48; c = -578;
Δ = b2-4ac
Δ = -482-4·1·(-578)
Δ = 4616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4616}=\sqrt{4*1154}=\sqrt{4}*\sqrt{1154}=2\sqrt{1154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{1154}}{2*1}=\frac{48-2\sqrt{1154}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{1154}}{2*1}=\frac{48+2\sqrt{1154}}{2}
$